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President Trump is five days into his term and there have been at least two instances in which he made statements that have not been backed up by any evidence.

The first was one about the size of the crowd at his inauguration — a topic that has raised questions for White House press secretary Sean Spicer as well. The second relates to unproven allegations of voter fraud, which he has stated before.

1. Trump Makes Unproven Claims About Inauguration Audience

The question of how many people attended Trump’s inauguration ceremony in person on Friday has been a hotly debated topic since it unfolded after photos of the National Mall from the vantage point of the Washington Monument were compared to that of former President Barack Obama’s first inauguration in 2009. The side-by-side photos showed the crowds gathered on the Mall as the inaugurations were underway.

Getty Images | Reuters

Jan. 20, 2009 Inauguration, 11AM | Jan. 20, 2017 Inauguration, 12PM

No official crowd counts were ever released because the National Park Service, which oversees the Mall, does not provide them.

That didn’t stop Trump from making his own estimates and sharing them when he went to CIA headquarters to speak to members of the intelligence community the next day.

“We had, it looked honestly, looked like a million and half people, whatever it was. But it went all the way back, to the back of the Washington Monument and by mistake I get this network [on TV] and it showed you an empty field, and it said we drew 250,000 people. Now, that’s not bad but it’s a lie. We had 250,000 people literally around in the little bowl that we constructed,” Trump said.

In his press briefing on Monday, Spicer defended his own earlier claim that it was the most-watched inauguration ever based on the cumulative number of people who watched it unfold in person as well as those who watched online, on television, or through streaming services. That total number of viewers has not been tabulated.

Damon Winter/The New York Times via Redux

President Donald Trump addresses the crowd at the U.S. Capitol in Washington, Jan. 20, 2017.

2. Trump Repeats His Earlier Unproven Claims That There Were Millions of Cases of Illegal Voting

During his first meeting with congressional leaders in the White House after his inauguration, Trump reportedly spent several minutes talking about the election results. Democratic and Republican sources familiar with the conversation told ABC News that as part of that discussion, Trump said that he lost the popular vote because of millions of illegal votes.

He specifically said that “3 to 5 million illegals” voted, according to two Democratic aides who spoke on condition of anonymity. A Republican House aide corroborated the account, but said the comments were made in jest during a jovial exchange with House Minority Leader Nancy Pelosi of California.

Today, House Speaker Paul Ryan was asked at a news conference about what Trump said, and Ryan responded that he did not want to get into a discussion on the topic but reiterated that he has not seen anything to back Trump’s claim.

“I have seen no evidence to that effect. I have made that very, very clear,” said Ryan, R-Wisc.

Spicer was pressed on the question of voter fraud during today’s press briefing and doubled down, calling it a “longstanding belief” that Trump holds.

“He continues to maintain that belief based on studies and evidence people have presented to him,” Spicer said of Trump.

“Anything’s possible, I think, at some point,” he added. “There is no investigation. I said it was possible. Anything is possible. It was a hypothetical question.”

This is not the first time that Trump has made this unsubstantiated claim. After he became president-elect, Trump posted at least two tweets about “serious voter fraud” and “millions of people who voted illegally.”

In addition to winning the Electoral College in a landslide, I won the popular vote if you deduct the millions of people who voted illegally

In December, then-Vice President-elect Mike Pence, defended Trump, citing a Pew study as the source for the “millions” who allegedly voted illegally.

But the Pew study’s primary author, David Becker, tweeted in response to references to his research: “As primary author of the report the Trump camp cited today, I can confirm the report made no findings re: voter fraud. We found millions of out of date registration records due to people moving or dying, but found no evidence that voter fraud resulted. Voter lists are much more accurate now than when we issued that study in 2012, thanks to the 20 states sharing data through @ericstates_info.”

In another tweet as president-elect, Trump wrote that there was “serious voter fraud in Virginia, New Hampshire and California.” There is no evidence to back up the claim, and it’s unclear why those states were singled out.

ABC News reached out to election officials in all 50 states shortly before Election Day and not one had any evidence or reason to believe that widespread voter fraud has or would occur in their states.